What is (\partial)/(\partial x)(-4y^3sin(4x)) ?

The answer to (\partial)/(\partial x)(-4y^3sin(4x)) is -16y^3cos(4x)

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(\partial)/(\partial x)(-4y^3sin(4x))

\frac{\partial}{\partial x} (- 4 y^{3} sin (4 x))

- 16 y^{3} cos (4 x)

Solution steps

\frac{\partial}{\partial x} (- 4 y^{3} sin (4 x))

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 4 y^{3} \frac{\partial}{\partial x} (sin (4 x))

Apply the chain rule:

cos (4 x) \frac{\partial}{\partial x} (4 x)

= cos (4 x) \frac{\partial}{\partial x} (4 x)

\frac{\partial}{\partial x} (4 x) = 4

= - 4 y^{3} cos (4 x) \cdot 4

Simplify

= - 16 y^{3} cos (4 x)

\frac{d}{d x} (sin (x) - csc (x))

\int (2 x^{2} - 3)^{2} d x

x \to 2 lim (\frac{x}{x - 2})

x \to \infty lim (x^{3})

cos (x) + i sin (x)

What is (\partial)/(\partial x)(-4y^3sin(4x)) ?
The answer to (\partial)/(\partial x)(-4y^3sin(4x)) is -16y^3cos(4x)